Chaos synchronization of Yin and Yang T-S fuzzy models of Hénon map system

Abstract

Based on the Chinese philosophy, Yin is the decreasing, negative, historical or feminine principle in nature, while Yang is the increasing, positive, contemporary or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. Since the discrete Hénon map system is an invertible map, Yin–Yang T-S fuzzy model of chaotic Hénon map systems with increasing and decreasing argument can be studied. The Yang T-S fuzzy model of chaotic Hénon map system is presented. The Yin T-S fuzzy model of chaotic Hénon map system and Yin T-S fuzzy rules are obtained by invertible matrix in linear system theory. Chaos synchronization of Yang T-S fuzzy model of Hénon map systems is achieved by parallel distributed compensation technique, and the fuzzy controller for chaos synchronization of Yin T-S fuzzy model of Hénon map systems is also obtained by invertible matrix in linear system theory. The design of the Yin fuzzy controller is fleetly obtained by the inverse of Yang fuzzy controller, the concern is the Yin chaotic system must be an inverse of the Yang chaotic system. T-S fuzzy model scheme is used in the nonlinear discrete chaotic map system, so the nonlinear discrete chaotic map system can be analyzed by linear system theory.